- #1
Asad Raza
- 82
- 3
What's the difference between activity of a radioactive sample and the decay constant. Both are measured in second inverse.
Please distinguish among the two?
Please distinguish among the two?
I don't think so; they wouldn't have the same units, for a start.sophiecentaur said:One is the first time derivative and the other is a second time derivative OR a first derivative of a first derivative.
Well observed. Some confusion arose from the term 'second time derivative' in post #3.mjc123 said:I don't think so; they wouldn't have the same units, for a start.
I agree. But rate of decay is not decay constant.sophiecentaur said:Rate of decay is rate of change of rate of events.
Dimensional analysis of the situation is perfectly consistent. No 'paradox'.
Exactly, the units for both are s-1. A second time derivative would have units s-2.sophiecentaur said:I can't see where the idea of "the same units" came from. How can they be the same units? The only similarity is the 'per second'.
This makes no sense to me. Rate of decay is the rate of occurrence of decay events, equal to the rate of change of the number of undecayed nuclei. This is a first time derivative. "Rate of change of rate of events" is how the activity changes with time. Because of the exponential form of the equation, this is proportional to the activity, and has the same decay constant. Is this what you meant (interpreting "decay" as "decrease in activity" rather than "nuclear decay events")?sophiecentaur said:Rate of decay is rate of change of rate of events.
As an example, You can express torque in J. That doesn't make torque an energy. Typically it is written as Nm to make it look different, but it has the same units as energy.sophiecentaur said:How can they be the same units?
No. It's there rate of decay of the rate of events. The term 'decay' doesn't refer to the radioactive fission event of an individual nucleus.mjc123 said:Rate of decay is the rate of occurrence of decay events,
Right. The dimensions are not the relevant argument here then.mfb said:As an example, You can express torque in J. That doesn't make torque an energy. Typically it is written as Nm to make it look different, but it has the same units as energy.
Length and height of an object have the same units, that does not mean they are the same.
Two different things can have the same units, in this case dimensional analysis alone doesn't work.
The activity is the (negative) first time-derivative of the number of radioactive atoms in the sample.
The decay constant can be calculated as activity divided by the number of atoms in the sample. Note that the number of atoms is dimensionless.
mfb said:but it has the same units as energy
Activity refers to the rate at which a radioactive substance decays, while decay constant is a measure of the probability that a specific type of atom will decay within a given period of time.
The activity of a radioactive substance is directly proportional to its decay constant. This means that as the decay constant increases, so does the activity, and vice versa.
No, activity and decay constant are not interchangeable. While they are related, they are measuring different aspects of radioactive decay and have different units of measurement.
No, the decay constant of a radioactive substance depends on its specific type of atom and can vary greatly between different substances.
Changes in temperature can affect the activity and decay constant of a radioactive substance. In general, higher temperatures can increase the rate of decay and therefore increase both the activity and the decay constant.